Families of Non-irup Instances of the One-dimensional Cutting Stock Problem Families of Non-irup Instances of the One-dimensional Cutting Stock Problem

In case of the one-dimensional cutting stock problem (CSP) one can observe for any instance a very small gap between the integer optimal value and the continuous relaxation bound. These observations have initiated a series of investigations. An instance possesses the integer roundup property (IRUP) if its gap is smaller than 1. It is well-known that there exist instances of the CSP having a gap greater than 1 but there is not known any instance with gap at least 2. In this paper we present families of non-IRUP instances and give methods to construct such instances. Furthermore, an equivalence relation for instances of the CSP is considered to become independent from the real size parameters.